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Simplifying x5 + -7x3 + -10x = 0 Reorder the terms: -10x + -7x3 + x5 = 0 Solving -10x + -7x3 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-10 + -7x2 + x4) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-10 + -7x2 + x4)' equal to zero and attempt to solve: Simplifying -10 + -7x2 + x4 = 0 Solving -10 + -7x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -7x2 + 10 + x4 = 0 + 10 Reorder the terms: -10 + 10 + -7x2 + x4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -7x2 + x4 = 0 + 10 -7x2 + x4 = 0 + 10 Combine like terms: 0 + 10 = 10 -7x2 + x4 = 10 The x term is -7x2. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x2 + 12.25 + x4 = 10 + 12.25 Reorder the terms: 12.25 + -7x2 + x4 = 10 + 12.25 Combine like terms: 10 + 12.25 = 22.25 12.25 + -7x2 + x4 = 22.25 Factor a perfect square on the left side: (x2 + -3.5)(x2 + -3.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x2 + -3.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x2 + -3.5 = 4.716990566 Simplifying x2 + -3.5 = 4.716990566 Reorder the terms: -3.5 + x2 = 4.716990566 Solving -3.5 + x2 = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = 4.716990566 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = 4.716990566 + 3.5 x2 = 4.716990566 + 3.5 Combine like terms: 4.716990566 + 3.5 = 8.216990566 x2 = 8.216990566 Simplifying x2 = 8.216990566 Take the square root of each side: x = {-2.866529359, 2.866529359}Subproblem 2
x2 + -3.5 = -4.716990566 Simplifying x2 + -3.5 = -4.716990566 Reorder the terms: -3.5 + x2 = -4.716990566 Solving -3.5 + x2 = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = -4.716990566 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = -4.716990566 + 3.5 x2 = -4.716990566 + 3.5 Combine like terms: -4.716990566 + 3.5 = -1.216990566 x2 = -1.216990566 Simplifying x2 = -1.216990566 Reorder the terms: 1.216990566 + x2 = -1.216990566 + 1.216990566 Combine like terms: -1.216990566 + 1.216990566 = 0.000000000 1.216990566 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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